{"id":9452,"date":"2022-08-30T09:32:51","date_gmt":"2022-08-30T09:32:51","guid":{"rendered":"https:\/\/www.prepbytes.com\/blog\/?p=9452"},"modified":"2023-04-27T13:12:38","modified_gmt":"2023-04-27T13:12:38","slug":"conversion-of-prefix-expression-to-infix-expression","status":"publish","type":"post","link":"https:\/\/prepbytes.com\/blog\/conversion-of-prefix-expression-to-infix-expression\/","title":{"rendered":"Conversion of Prefix expression to Infix expression"},"content":{"rendered":"

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Conversion of prefix expression to infix expression involves rearranging the operators and operands to follow the rules of infix notation while maintaining the order of operations. This can be achieved through recursive parsing of the prefix expression.<\/p>\n

How to Convert Prefix to Infix?<\/h2>\n

You are given an arithmetic expression. Your task is Convert an arithmetic expression in prefix notation into the equivalent infix notation.<\/p>\n

Sample Example :<\/strong><\/p>\n

Prefix Input : *-a\/bc-\/ade\nInfix output : ((a-(b\/c))*((a\/d)-e))\nPrefix input : *ab\nInfix expression : (a*b)<\/code><\/pre>\n
Introduction to Arithmetic Notations<\/h2>\n
Any arithmetic expression consists of operands and operators. Notation is how we arrange our operators and operands to write the arithmetic expression.<\/p>\n
There are three different notations for writing the Arithmetic expression :<\/p>\n
    \n
  • \n
    Infix expression:<\/strong> An infix expression is a mathematical or logical expression in which operators are written between the operands.<\/p>\n
    For example<\/strong> => a + b * c Infix expressions are easy to read, write and understand by humans, but not by computer It\u2019s costly, in terms of time and space, to process Infix expressions.<\/p>\n<\/li>\n
  • \n
    Postfix expression:<\/strong> It is also known as Reverse Polish Notation. An expression is said to be in postfix notation if the operators in the expression are placed after the operands on which the operator works.<\/p>\n
    For example<\/strong> => abc*+ It\u2019s the most used notation for evaluating an arithmetic expression<\/p>\n<\/li>\n
  • \n
    Prefix expression:<\/strong> It is known as Polish Notation. An expression is said to be in prefix notation if the operators in the expression are placed before the operands on which the operator works.<\/p>\n
    For example<\/strong> => +a*bc<\/p>\n<\/li>\n<\/ul>\n
    Precedence Order and Associativity of Operators<\/h3>\n\n
    Precedence<\/td>Type<\/td>Operators<\/td>Associativity<\/td><\/tr>
    1<\/td>Postfix<\/td>() [] -> . ++ —<\/td>Left to Right<\/td><\/tr>
    2<\/td>Unary<\/td>+ – ! ~ ++ — (type)* & sizeof<\/td>Right to Left<\/td><\/tr>
    3<\/td>Multiplicative<\/td>* \/ %<\/td>Left to Right<\/td><\/tr>
    4<\/td>Additive<\/td>+ –<\/td>Left to Right<\/td><\/tr>
    5<\/td>Shift<\/td><<, >><\/td>Left to Right<\/td><\/tr>
    6<\/td>Relational<\/td>< <= > >=<\/td>Left to Right<\/td><\/tr>
    7<\/td>Equality<\/td>== !=<\/td>Left to Right<\/td><\/tr>
    8<\/td>Bitwise AND<\/td>&<\/td>Left to Right<\/td><\/tr>
    9<\/td>Bitwise XOR<\/td>^<\/td>Left to Right<\/td><\/tr>
    10<\/td>Bitwise OR<\/td>|<\/td>Left to Right<\/td><\/tr>
    11<\/td>Logical AND<\/td>&&<\/td>Left to Right<\/td><\/tr>
    12<\/td>Logical OR<\/td>||<\/td>Left to Right<\/td><\/tr>
    13<\/td>Conditional<\/td>?:<\/td>Right to Left<\/td><\/tr>
    14<\/td>Assignment<\/td>= += -+ *= \/= %= >>= <<= &= ^= |=<\/td>Right to Left<\/td><\/tr>
    15<\/td>Comma<\/td>,<\/td>Left to Right<\/td><\/tr><\/tbody><\/table><\/figure>\n\n
    Approach for Prefix to Infix Converter<\/h3>\n
    Here, is the prefix to infix using stack. The stack helps us store the operands. Whenever an operator is found, we pop two operands from the stack and push a new operand, which is the result of the current operator on the popped operands, into the stack with parenthesis. The final element at the top of the stack will be our infix expression.<\/p>\n
    Algorithm for Prefix to Infix Converter<\/h3>\n
    Here, is the algorithm for prefix to infix converter:<\/p>\n
      \n
    • Start scanning the prefix expression from right to left.<\/li>\n
    • If the current character is an operand (a number or a variable), push it onto a stack.<\/li>\n
    • If the current character is an operator (+, -, *, \/, ^), pop two operands from the stack and concatenates them with the operator in between to form an infix sub-expression. Then push the infix sub-expression onto the stack.<\/li>\n
    • Repeat steps 2 and 3 until the entire prefix expression has been scanned.<\/li>\n
    • The final infix expression will be the only item remaining on the stack.<\/li>\n<\/ul>\n
      NOTE:<\/strong> \u2018+\u2019 denotes the concatenation of strings.<\/p>\n
      Prefix to Infix Conversion Example with Dry Run<\/h3>\n
      \"\"<\/p>\n
      Code Implementation<\/h3>\n\t\t\t\t\t\t